---
title: "Filling the Gaps of Polarity: Implementing Dependent Data and Codata Types with Implicit Arguments"
url: https://daily.dev/posts/filling-the-gaps-of-polarity-implementing-dependent-data-and-codata-types-with-implicit-arguments-x0jqzpwlf
source_url: https://programming-journal.org/2025/10/19/
type: article
source: "The Programming Journal"
published: 2025-11-19T19:29:12.223Z
updated: 2025-12-08T02:20:14.422Z
tags: ["compiler", "functional-programming", "type-systems"]
reading_time: 2
upvotes: 0
comments: 0
language: en
---

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# Filling the Gaps of Polarity: Implementing Dependent Data and Codata Types with Implicit Arguments

**[The Programming Journal](https://daily.dev/sources/programming-journal)** · 2 min read · 0 upvotes · 0 comments

## Summary

Researchers present an algorithmic type system and unification algorithm for Polarity, a dependently typed language that treats inductive (data) and coinductive (codata) types symmetrically. The work addresses the expression problem by enabling both pattern matching extensibility and interface-based extensibility while adding support for implicit arguments. The paper provides comprehensive algorithms for reduction semantics, conversion checking, and pattern-matching unification that maintain the language's core symmetry between data and codata types.

## Full article

daily.dev links to this article rather than hosting it. Read it at the original source: <https://programming-journal.org/2025/10/19/>

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---

Tags: [#compiler](https://daily.dev/tags/compiler), [#functional-programming](https://daily.dev/tags/functional-programming), [#type-systems](https://daily.dev/tags/type-systems)

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